In a small saucepan, melt the butter and chocolate, then take it off the heat and let it cool.
Preheat the oven to 180C degrees. Line a 20x20 baking dish with parchment paper.
Whisk the eggs, sugar and vanilla essence with an electric mixer until light and fluffy. Add the cooled chocolate sauce, then sieve the flour into the mixture while gently stirring the batter.
Fold in the white chocolate pieces, then pour the mixture into the baking dish, spreading it out evenly.
Bake for 25-30 minutes until the top is cooked but the middle is still a bit gooey.
Let the cake cool in the tin for 10 minutes, then transfer it to a wire rack.
Let it cool completely before cutting into squares (you might want to put it the fridge for an hour or freezer for 15 minutes before slicing in order avoid crumbles). Dust with icing sugar, if liked.